Determine f(x) if f'(x) is (5x-3)/(x^2+4)

To determine the function f(x), we'll have to
integrate  (5x-3)/(x^2+4)

Int  (5x-3)dx/(x^2+4) = f(x) +
C

We'll use the additive property of the
integral:

Int  (5x-3)dx/(x^2+4) = Int 5xdx/(x^2+4) - Int
3dx/(x^2+4)

We'll note Int 5xdx/(x^2+4) = 5
I1

                 Int 3dx/(x^2+4) =
3I2

We'll calculate I1 using substitution
technique.

We'll note x^2+4 =
t

We'll differentiate both
sides:

2xdx = dt

We'll
substitute in the original integral and we'll get:

I1 = Int
dt/t

I1 = ln |t| + C, but t = x^2+4 >
0

I1 = ln (x^2+4) + C

5I1 =
5ln (x^2+4) + C

5I1 = ln (x^2+4)^5 +
C

We'll calculate
I2:

I2 = Int dx/(x^2+4)

I2  =
[arctan (x/2)]/2 + C

3I2 = 3[arctan (x/2)]/2
+ C

Int  (5x-3)dx/(x^2+4) = ln
(x^2+4)^5 + 3[arctan (x/2)]/2 + C

What is the inverse of the function f(x) = [(lnx)-5]/2

Given the function f(x) = [ln(x)] - 5
/2

We need to find the inverse function f^-1
(x).

Let y= [ln(x) -5)/2

We will need
to isolate x.

First we will multiply by
2.

==> 2y= ln x - 5

Now we will
add 5 to both sides.

==> 2y + 5 = ln
x

Now we will rewrite into exponent
form.

==> x= e^(2y+5)

Now we
will replace x and y.

==> y=
e^(2x+5)

Then the inverse function
is:

f^-1 (x) =
e^(2x+5)

In The Kite Runner, what does Amir say about clichés?

This section of the novel comes in Chapter Fifteen, when
Amir goes to Pakistan to meet with Rahim Khan who is close to death. Amir tells us about
what he was taught about the use of cliches in creative writing and then he goes on to
defend his use of the cliche "the elephant in the room" to describe his meeting with
Rahim Khan after so long and how awkward it was. Note what he says about
cliches:

A
creative writing teacher at San Jose State used to say about clichés: "Avoid them like
the plague." Then he'd laugh at his own joke. The class laughed along with him, but I
always thought clichés got a bum rap. Because, often, they're dead-on. But the aptness
of the clichéd saying is overshadowed by the nature of the saying as a cliché. For
example, the "elephant in the room" saying. Nothing could more correctly describe the
initial moments of my reunion with Rahim
Khan.

Therefore Amir defends
his use of clichés and in particular his description of his reunion with Rahim Khan by
arguing that clichés have become clichés for a reason. They correctly sum up a
situation, as in this case both Rahim Khan and Amir initially try to ignore the elephant
in the room.

What is the opression in "The Story of an Hour" and "A Doll's House"?

This is a great question! There are lots of ways that you
can compare and contrast the two central protagonists in these texts, Mrs. Mallard and
Nora. However, the wording of your question seems to identify the central way that you
can explore their presentation. Both characters are oppressed females in a patriarchal
world full of patriarchal institutions, especially marriage, that force them to become
something that they are not. Likewise, both characters experience liberation through the
action of the story, although in the case of Mrs. Mallard, this liberty is short-lived.
Both reveal that the patriarchal institution of marriage has the potential to squash and
inhibit the growth, maturity and development of a female from occurring along natural
lines, as the wife has to meet a whole host of societal expectations to fulfil her
"role" as wife.

Therefore, if you are writing an essay on
this topic, I would explore the nature of the word "oppression" as applied in this case
and the way that both characters reveal. Then I would consider how Nora and Mrs. Mallard
gain liberation. Hopefully the points I have given you above will give you lots of ideas
for what you can talk about. Good luck!

What kind of person do you think Boo Radley is? Why?

Who knows what was going on inside of Boo Radley's head.
(It would be a great question for author Harper Lee to answer herself.) I believe it's
obvious that Boo didn't eat raw squirrels or cats, and he probably did no physical harm
to anyone until he met up with Bob Ewell. Mentally instability no doubt hounded this
very shy and gentle man. Of all the accusations made against Boo, his nocturnal
sightings and habits may have had some validity; no better proof is evident than when
he warmed Scout with a blanket and suddenly appeared to save the children from Bob. Boo
must have seen himself as a protector of his young neighbors, and they brought out his
curious nature for a while. Once they were safe from Ewell, Boo retreated back into the
Radley House, rarely to be seen again.

What are Tom's dreams?

Tom's dream in The Glass Menagerie is basically to run
away from the alleyway apartment and the oppression that his family has him under and be
free to write poetry, read literature, and experience the adventures that he sees in the
movie theatre where he goes to escape from everyday
life.

Tom is a born poet, which is a huge contrast from his
rogue-type job at the factory, where darkness, and a harsh environment are the rule.
Instead, Tom imagines beauty, adventure, color, and freedom. These are his mechanisms of
escapism and is meant to contrast his reality versus his
fantasy.

Show how Shelley's use of language (in Frankenstein) reveals that Victor's dreams have been shattered (when the creature comes to life).

Mary Shelley uses very dramatic and imagery-laden language to
define the shattering of Victor's dreams in her novel Frankenstein. Chapter
four of the novel defines Victor's dreams regarding his "son."

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A new species would bless me as its creator and source;
many happy and excellent natures would owe their being to me. No father could claim the gratitude
of his child so completely as I should deserve
theirs.

Typical of the "new parent,"
Victor's dreams (regarding his son) is that he is able to create a life which would denote him
(Victor) as the most gracious being on earth. It is, undeniably, his dream to birth a child who
will look up to him, as the father. This dream further developed through Victor's meticulous
nature in creating his "son."

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After having formed this determination, and having spent
some months in successfully collecting and arranging my materials, I
began.

To Victor's dismay and horror,
his "son" is not what he dreamt of. Instead, the being is large, ugly, and
horrifying.

How can I
describe my emotions at this catastrophe, or how delineate the wretch whom with such infinite
pains and care I had endeavoured to
form?

Essentially, in the end, the
physical attributes of Victor's son shattered his dream. His son was not beautiful; instead, the
creature was horridly ugly, inarticulate, and horrifying.